matita/matita/contribs/lambdadelta/basic_2/rt_computation/lsubsx_rdsx.ma

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  13 (**************************************************************************)
  14
  15 include "basic_2/rt_computation/rdsx_drops.ma".
  16 include "basic_2/rt_computation/rdsx_lpxs.ma".
  17 include "basic_2/rt_computation/lsubsx.ma".
  18
  19 (* CLEAR OF STRONGLY NORMALIZING ENTRIES FOR UNBOUND RT-TRANSITION **********)
  20
  21 (* Properties with strongly normalizing referred local environments *********)
  22
  23 (* Basic_2A1: uses: lsx_cpx_trans_lcosx *)
  24 lemma rdsx_cpx_trans_lsubsx (h):
  25       ∀G,L0,T1,T2. ⦃G, L0⦄ ⊢ T1 ⬈[h] T2 →
  26       ∀f,L. G ⊢ L0 ⊆ⓧ[h, f] L →
  27       G ⊢ ⬈*[h, T1] 𝐒⦃L⦄ → G ⊢ ⬈*[h, T2] 𝐒⦃L⦄.
  28 #h #G #L0 #T1 #T2 #H @(cpx_ind … H) -G -L0 -T1 -T2 //
  29 [ #I0 #G #K0 #V1 #V2 #W2 #_ #IH #HVW2 #g #L #HK0 #HL
  30   elim (lsubsx_inv_pair_sn_gen … HK0) -HK0 *
  31   [ #f #K #HK0 #H1 #H2 destruct
  32     /4 width=8 by rdsx_lifts, rdsx_fwd_pair, drops_refl, drops_drop/
  33   | #f #K #HV1 #HK0 #H1 #H2 destruct
  34     /4 width=8 by rdsx_lifts, drops_refl, drops_drop/
  35   ]
  36 | #I0 #G #K0 #T #U #i #_ #IH #HTU #g #L #HK0 #HL
  37   elim (lsubsx_fwd_bind_sn … HK0) -HK0 #I #K #HK0 #H destruct
  38   /6 width=8 by rdsx_inv_lifts, rdsx_lifts, drops_refl, drops_drop/
  39 | #p #I0 #G #L0 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #f #L #HL0 #HL
  40   elim (rdsx_inv_bind … HL) -HL
  41   /4 width=2 by lsubsx_pair, rdsx_bind_void/
  42 | #I0 #G #L0 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #f #L #HL0 #HL
  43   elim (rdsx_inv_flat … HL) -HL /3 width=2 by rdsx_flat/
  44 | #G #L0 #V #U1 #T1 #T2 #HTU1 #_ #IHT12 #f #L #HL0 #HL
  45   elim (rdsx_inv_bind … HL) -HL #HV #HU1
  46   /5 width=8 by rdsx_inv_lifts, drops_refl, drops_drop/
  47 | #G #L0 #V #T1 #T2 #_ #IHT12 #f #L #HL0 #HL
  48   elim (rdsx_inv_flat … HL) -HL /2 width=2 by/
  49 | #G #L0 #V1 #V2 #T #_ #IHV12 #f #L #HL0 #HL
  50   elim (rdsx_inv_flat … HL) -HL /2 width=2 by/
  51 | #p #G #L0 #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #f #L #HL0 #HL
  52   elim (rdsx_inv_flat … HL) -HL #HV1 #HL
  53   elim (rdsx_inv_bind … HL) -HL #HW1 #HT1
  54   /4 width=2 by lsubsx_pair, rdsx_bind_void, rdsx_flat/
  55 | #p #G #L0 #V1 #V2 #U2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #HVU2 #f #L #HL0 #HL
  56   elim (rdsx_inv_flat … HL) -HL #HV1 #HL
  57   elim (rdsx_inv_bind … HL) -HL #HW1 #HT1
  58   /6 width=8 by lsubsx_pair, rdsx_lifts, rdsx_bind_void, rdsx_flat, drops_refl, drops_drop/
  59 ]
  60 qed-.
  61
  62 (* Advanced properties of strongly normalizing referred local environments **)
  63
  64 (* Basic_2A1: uses: lsx_cpx_trans_O *)
  65 lemma rdsx_cpx_trans (h):
  66       ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬈[h] T2 →
  67       G ⊢ ⬈*[h, T1] 𝐒⦃L⦄ → G ⊢ ⬈*[h, T2] 𝐒⦃L⦄.
  68 /3 width=6 by rdsx_cpx_trans_lsubsx, lsubsx_refl/ qed-.
  69
  70 lemma rdsx_cpxs_trans (h):
  71       ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 →
  72       G ⊢ ⬈*[h, T1] 𝐒⦃L⦄ → G ⊢ ⬈*[h, T2] 𝐒⦃L⦄.
  73 #h #G #L #T1 #T2 #H
  74 @(cpxs_ind_dx ???????? H) -T1 //
  75 /3 width=3 by rdsx_cpx_trans/
  76 qed-.